Try to create a new profile as a test to check if your current profile is causing the problems.
See "Creating a profile":
*https://support.mozilla.org/kb/profile-manager-create-and-remove-firefox-profiles
*http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Profile_issues
If the new profile works then you can transfer some files from an existing profile to the new profile, but be careful not to copy corrupted files.
*http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox